I can't render animation in Blender with the rendered model and a picture background
I suggest you familiarize yourself a bit more with the software. The background images you see in the 3d viewport will NEVER be rendered. In order to get a background image you can use the compositor:

How to composite in a background picture?

As for the rendering to black screen, check the compositor as well (is everything set up correctly) and check if the light sources work. (This you can check in the viewport by changing to the cycles preview)

What does the Render and Preview of the Samples section do?

a relevant tutorial is 
here